A $2 \,{kg}$ steel rod of length $0.6\, {m}$ is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is $\ldots \ldots \ldots \ldots \,{ms}^{-1}$. (Take $g = 10\, {ms}^{-2}$ )
$6$
$60$
$0.6$
$3600$
A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega$. Its centre of mass will rise upto maximum height :-
Two uniform similar discs roll down two inclined planes of length $S$ and $2S$ respectively as shown is the fig. The velocities of two discs at the points $A$ and $B$ of the inclined planes are related as
A circular disc of mass $2 \,kg$ and radius $10 \,cm$ rolls without slipping with a speed $2 \,m / s$. The total kinetic energy of disc is .......... $J$
A rolling wheel of $12 \,kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \,kg$ through a string of fixed length and pulley as shown in figure. Consider $PR$ as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom $Q$ of the inclined plane $P Q$ will be $\frac{1}{2} \sqrt{ xgh } \,m / s$. The value of $x$ is.............
A ring, a solid sphere and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest